FIRST Minister Nicola Sturgeon has issued another warning to supporters over their online behaviour, speaking out after Scotland's last minute defeat to Australia in the quarter-final of the Rugby World Cup.

Although Ms Sturgeon did not make reference to any one tweet or tweeter, it appears to have been sparked by an exchange involving the author JK Rowling and pro-independence blogger Wings Over Scotland.

Posting on her @NicolaSturgeon Twitter handle, she said "people who disagree are not anti-Scottish".

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In one Tweet, after Ms Rowling said Scotland had been "magnificent" in the game and "did us proud", Wings Over Scotland writer Stuart Campbell questioned her right to support the team, writing: "You don't think we're a nation at all."

The author had been a high-profile supporter of the No campaign during the referendum.

In response, Ms Rowling Tweeted: "I know Scotland's a nation. I live there, you see. I pay tax there and I contribute more than bile there."

The exchanges also involved broadcaster and journalist Muriel Gray and crime writer Val McDermid.

It comes as World Rugby admitted referee Craig Joubert blundered by awarding Australia the last-gasp penalty that sent Scotland out of the World Cup.

Scotland led 34-32 at Twickenham when Jon Welsh was ruled deliberately offside for playing the ball after a knock-on by a team-mate.

The sport's governing body said in a statement that having reviewed the incident and as Wallabies player Nick Phipps had touched the ball the "appropriate decision was a scrum to Australia for the original knock-on" and not a penalty.

Ms Sturgeon's full tweet read: "Note to my fellow independence supporters. People who disagree are not anti Scottish. Does our cause no good to hurl abuse (& it's wrong)."

She also re-tweeted Ms McDermid who said in one of her postings: "I for one am proud to call @jk_rowling and @ArtyBagger [Muriel Gray] my fellow countrywomen."

In June, Ms Sturgeon warned so-called "cybernats'' who are members of the SNP that they could be disciplined by the party.

Writing in the Daily Mail, she said it was ''not acceptable'' for people to use social media to ''threaten violence, or hurl vile abuse, or seek to silence the voice of others through intimidation''.

Scottish Liberal Democrat leader Willie Rennie MSP said: "This is not new and not the first time that Nicola Sturgeon has reprimanded her own supporters for their online abuse but it is refreshing none the less as they used to deny that there was ever a problem.

"This reveals the scale of the problem for the nationalist movement which has been infected by large numbers of people who believe the way to win an argument is to be offensively aggressive online."

Meanwhile, Prime Minister David Cameron said Scotland's rugby team performed more bravely and boldly than any performance he has seen.

Mr Cameron described the team's performance in the quarter final defeat  as "remarkable" and revealed he was heartbroken at the result.

During a Commons statement, Mr Cameron offered his commiserations to the team.

He went on: "They really played like lions, I don't think I've seen a braver, more bold performance, it was remarkable to see."